I would like to make my images 'sharper' / 'clearer' with more detail and color and was wondering if this if more of a Equipment issue or rather more of processing the images with different techniques?

Maybe a combination of both taking a good photo and then processing it. I know some possibilities include HDR, Tonal Mapping, Photoshop Actions (custom effects), and better equipment (camera sensor) But what about lenses, and filters (don't think filters apply as much)

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Everything is cumulative. This applies to things which contribute to both sharpness and softness. So to maximize sharpness and color-detail, you need to improve as many aspects as possible:

Stability. A good tripod ensures your camera does not move during the exposure. Ideally you are also triggering the camera remotely or with a delay and mirror-lockup (for SLRs).

Low ISO. Using a lower ISO and the standard range of your camera means less noise that eat away details.

Good sensor with large pixels. Larger pixels have higher signal-to-noise ratio (S/N) which makes less noise.

Sharp lens stopped down to optimal aperture. The quality of lenses differs enormously and very sharp lenses can out-resolve most camera sensors but even top-quality lenses have an optimal aperture, usually stopped-down a bit from the maximum but without reaching the diffraction limit which causes global softness.

Accurate focus. When using AF, it is possible that the camera does not focus exactly where it should. Higher-end models can be calibrated to fix per-lens issues. When manual focusing, a specialized focus-screen can make it easier.

Good processing, either in-camera (JPEG) or in-computer (RAW). The defaults JPEG parameters are often a tad soft due to overly aggressive noise-reduction (All digital cameras apply noise-reduction to JPEG images. Some due it to RAW files too). These are only defaults and can be changed on all DSLRs and most SLDs to produce much sharper and cleaner results.

Filters rarely apply because the add an element in the optical path which introduces inter-reflections, flare and may even reduce sharpness. Even the best filters have such effect. In some cases a filter can cut-down on haze which makes distance objects more crisp but this is a case-by-case compromise to measure.

Processing is tricky when it comes to noise and details. While reducing noise, details tend to go away, making images look softer. There are plenty of software using different noise-reduction algorithms and each one has their favorite based on how the perceive and output their images.

The are more advanced techniques such as image stitching (usually done for panoramas) and super-resolution to increase resolution and sharpness by using multiple images as input. These can give extremely clean and sharp images when done right.